On the Minimum Size of a Point Set Containing a 5-Hole and Double Disjoint 3-Holes

Let $n(k,l,m)$, $k\leq l\leq m$, be the smallest integer such that any finite planar point set of at least $n(k,l,m)$ points in general position, contains an empty convex $k$-hole; an empty convex $l$-hole and an empty convex $m$-hole, which are all pairwise disjoint. In this paper we prove that $n(3,3,5)=12$.